Analog Circuits Seth Price Department of Chemical Engineering New Mexico Tech Rev. 1/13/16

Ohm’s Law E = IR – E is the voltage across a component – I is the current through a component – R is the resistance of the component

Resistor Color Code

Series/ Parallel Combinations Series: the same current passed through multiple components Req = R1 + R2 + … Parallel: the same voltage is across multiple components 1/Req = 1/R1 + 1/R2 + ….

Kirchoff’s Current Law (KCL) Any current flowing into a node must also leave the node: – The sum of all currents = 0 – Think “conservation of mass”

Kirchoff’s Voltage Law (KVL) The sum of the voltages around any closed loop must equal zero – Any voltage generated must be dissipated – Think “conservation of mass”

Using a Multimeter Measure voltage in parallel – Meter tries to have infinite impedance Measure current in series – Meter tries to have no impedance 3 Point Safety Check – Measure known voltage (ex wall outlet) – Measure voltage on what you think has no power – Measure known voltage again

Current Limiter All devices have a maximum allowable current A resistor in series drops current in loop

Shunt Resistor High currents are hard to measure Instead, place a small resistance (of known value) in series Measure voltage drop across resistor From Ohm’s law: I= V/R

Wheatstone Bridge Easy to detect small voltages R1, R2 and R3 are known Rx is adjustable – Perhaps a sensor As Rx changes, the current from A->C changes, Vg changes

Diodes (PN Junction) Diodes conduct in only one direction Semiconducting device Resistance is non-linear Require a “knee” or “turn-on” voltage – Silicon: V – Germanium: 0.3V – LED: 1.7V

Diode Vs. Sine Wave content/uploads/2009/08/23-half-wave-rectifier-1024x368.gif

IV Curve for Diodes

Capacitors Store energy in an electric field Measured in Farads (F) Two physical configurations – Parallel plates – Concentric cylinders

Capacitor Combinations Series Combination: 1/C eq = 1/C 1 + 1/C 2 + … + 1/C n Parallel Combination: C eq = C 1 + C 2 + … + C n

Capacitor Voltage Vc(t): Voltage across capacitor at any time Vs: Source voltage T: Time constant t: elapsed time V c(t) = V s (1-e -t/T )

Inductors Store energy in a magnetic field Measured in Henries (H) Typically a coil of wire Adjustable inductor: slug

Inductor Combinations Series Combinations L eq = L 1 + L 2 + … + L n Parallel Combinations 1/L eq = 1/L 1 + 1/L 2 + … + 1/L n

Inductor Voltage V(t): Voltage across Inductor as a function of time L: inductance in Henries di/dt: change in current with respect to time V(t) = -L * di/dt

Time Constants Time Constant (T): way to characterize time to charge/discharge a capacitor or inductor 1*T: 63% of the maximum charge 5*T: fully charged For a capacitor: T = R*C For an inductor: T = L/R

Solenoids Changing current induces magnetic field Magnetic field moves plunger Used in starter motors, valves, latches, etc.

Solenoid Valve

Transformers Two adjacent inductors that can influence each other Can add an iron core to transformer to increase magnetic field No electron travels between inductors – Isolation Transformer

Putting it all together… DC Power Supply